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0223U001314,
0118U003012
,
Methods and models of statistical physics to describe the emergence of structures and explanations of scaling in complex systems
Holovatch Yurii V., Доктор фізико-математичних наук
Kozlovskyi Mykhailo P., д.ф.-м.н.
27-01-2023
Institute of Condensed Matter Physics of the National Academy of Sciences of Ukraine
The critical behavior of complex structurally disordered and anisotropic magnets is studied. Universal parameters determining the critical behavior of such materials are calculated. The critical behavior that occurs in lattice gas models with restrictions is studied, simulating catalytically activated reactions of molecules that remain chemically inactive in the absence of such restrictions. The emergence of scaling laws describing the statistical properties of systems of interacting agents on complex networks is analyzed. Traditional models of statistical physics are considered as well as statistical features of social and transport networks and problems of scientometrics are analyzed. The behavior of a simple fluid, including the region of the critical point, is studied using several theoretical models: the Morse fluid model, which describes properties of a number of real substances and for which the results of numerical calculations are known, and the model with the Curie-Weiss interaction potential, which has an exact solution. The critical behavior of strongly anisotropic systems at the Lifshitz point in higher orders of the perturbation theory, as well as the peculiarities that arise in such systems when they are spatially confined, are investigated. New Feynman diagrams, which have not yet been considered in the theory of critical phenomena at the Lifshitz point, are calculated.
Dobush Oksana A.
Dudka Maxym L.
Krasnytska Mariana B.
Mryglod Olesya I.
Pylyuk Ihor V.
Sarkanych Petro V.
Shapoval Dmytro Yu.
Shpot Mykola A.
2023-01-27
Updated: 2025-12-06
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